You're right, and you're wrong.
IAC owned both Match and HatchLabs (which developed Tinder in 2012). They were later merged into one entity, and even later spun off from IAC altogether. They were "part of the same company" in that giant mega-corp super conglomerate owned both, but practically they were fully separate entities when Tinder was created. Match didn't buy Tinder, but it was merged with Tinder by parent company, just like OkCupid was acquired by IAC and merged with Match.
I mean, I was trying to keep it simple. :) I suppose it all comes down to what you mean by "fully separate entities"... but at the end of the day it was all under IAC. The corporate control and reporting structure went up to the CEO and board of IAC. Hatch Labs was an incubator IAC created specifically for developing things like Tinder. Yes Tinder got reshuffled and eventually it was all spun off but Tinder started under the same roof as Match. It wasn't bought.